Renewed signs that key figures in Muammar Gaddafi's regime are seeking an end to the crisis emerged on Sunday when the deputy foreign minister, Abdul Ati al-Obeidi, flew to Greece using the same route out as defector and his former boss, Moussa Koussa apparently with a message from the Libyan government seeking a way out of the crisis.

After meeting Obeidi Greece's foreign minister, Dimitris Droustas said: "From the Libyan envoy's comments it appears that the regime is seeking a solution." Droustas added that Greek officials had underlined the international community's call for Gaddafi to end hostilities.

The message, Droustas said, was: "Full respect and implementation of United Nations decisions, an immediate ceasefire, an end to violence and hostilities, particularly against the civilian population of Libya."

In a further sign of willingness within the regime to negotiate an end to the crisis, it was also claimed that Saif al-Islam, one of Gaddafi's sons and a pivotal figure in the regime, was proposing a compromise resolution to the country's civil war involving the Libyan leader relinquishing power to a new constitutional democracy.

Saif was said to be suggesting a transition under his direction as a possible way out of the impasse between the regime, in Tripoli, and the rebel forces in Benghazi.

The report coincided with another from a well-placed Arab source of an approach by Gaddafi to the former UN secretary-general, Kofi Annan. Gaddafi is said to have offered political reforms during a transition period overseen by one of his sons, the source said. Annan was involved in important aspects of bringing Libya in from the cold during his decade running the UN from 1997 to 2007.

Saif's move followed a visit to London by Mohammed Ismail, a key Gaddafi aide, revealed by the Guardian on Friday, to explore possible exit strategies for the Libyan regime.

The diplomatic moves came as a Turkish effort to assist civilians trapped in western Libya brought a reminder of the plight of Libyans on the ground. A Turkish ship that sailed into Misrata to rescue about 250 wounded people had to leave after crowds pressed forward on the quayside.

"It's a very hard situation … We had to leave early," Turkish consular official Ali Akin told Reuters after the ship stopped to pick up more wounded in the eastern rebel stronghold, Benghazi. Turkey's foreign minister ordered the ship into Misrata after it spent four days waiting for permission to dock. It arrived under cover from 10 Turkish air force F-16 fighters and two navy frigates. Misrata, Libya's third city, rose up with other towns against Gaddafi's rule in mid-February, but it is now surrounded by government troops. After weeks of shelling and encirclement, Gaddafi's forces appear to be gradually loosening the rebels' hold on the city.

David Cameron has sent a small Foreign Office team to Benghazi to undertake further consultations with rebels on a possible ceasefire and the makeup of a new government in the event of Gaddafi leaving. The team, led by the British ambassador to Italy, Christopher Prentice, arrived in Benghazi on Saturday, leaving Richard Northern, the British ambassador to Tripoli, in London to oversee operations. Prentice has spent much of his career in the Middle East including Iraq and Jordan.

British officials want to know more about the nature of the transitional council, its accountability, and whether it would give Gaddafi safe passage out of the country rather than force him to face trial. It would also discuss the prospect of arming the rebels, but the foreign secretary, William Hague, said on Sunday that Britain was unlikely to be involved in this.

With Hague due to make a statement on last week's defection of Libya's foreign minister, Moussa Koussa, other defections and the general state of the civil war, it was reported that Obeidi would travel next to Turkey and Malta, in a sign that Gaddafi's regime may be softening. Reports out of Tunisia had noted that Obeidi left Libya via Tunisia, the same route taken by Koussa. Obeidi, the Libyan minister of European affairs, had previously accompanied Koussa to the Tunisian town of Djerba last Wednesday but returned to Tripoli while Koussa flew on to London.

A former prime minister, Obeidi is a highly trusted figure and veteran of some of the most sensitive chapters of his country's recent diplomatic history. He negotiated the controversial release of the Lockerbie bomber, Abdelbaset al-Megrahi, in 2009.

Officials in Greece said there had been high-level contacts with Britain, Qatar and Libya before Obeidi's mission to Athens.

There have been widespread rumours since Koussa's defection last week that other senior officials may follow. The speculation has been encouraged by western governments, which see the implosion of the regime as desirable. The Nato-led coalition currently undertaking air strikes against the Libyan military has been divided over whether regime change is a legitimate goal.

According to a report in the New York Times, Saif al-Islam – who holds no formal position – is proposing a transition to a constitutional democracy under his direction. However, British sources have stressed there is no suggestion that Gaddafi is willing to accept the proposal.

With MI6 heavily involved in an effort to destabilise the regime, the rumours of deals being offered by senior Gaddafi figures are hard to verify.

The Interim National Council, which is heading the rebellion, has insisted that Gaddafi must relinquish power and is unlikely to accept his family's involvement in a move to a new government.

Although Saif has launched belligerent attacks on the uprising in the east and has publicly pledged that his family will "live and die in Libya", some see him as more pragmatic than his father. He has had a long association with western figures, including Tony Blair and Lord Mandelson, and studied at the LSE. Hague insisted it was right to let former Libyan intelligence chief Koussa come to Britain, and denied there had been any deal involving his asylum.

He said his officials would meet Scottish police today to discuss when they would be allowed to interview Koussa about the Lockerbie bombing and other crimes, saying: "We want more information about past events."

The Foreign Office said only that Koussa would be "entitled to apply for asylum".

But Tory MP Ben Wallace, parliamentary aide to justice secretary Ken Clarke, told the Mail on Sunday: "This man should not be granted asylum or any other special treatment. The only proper outcome is to bring him to justice."

Hague declined to say whether Koussa had been contacting ex-colleagues urging them to follow his example.

"I think that when someone like that says they want to get out it would be quite wrong to say no, you have got to stay there," he told the BBC's Andrew Marr Show.

He said he did not believe that the conflict would end in a stalemate. "Let's be clear, if the Libyan regime tries to hang on in this situation, they are internationally isolated, they can't sell any oil," he said.

"There is no future for Libya on that basis, and so I think even the prospect of stalemate should encourage people in Tripoli to think, 'Well, Gaddafi has now got to go.'"

In December 2010, a man in Tunisia burned himself to death in protest at his treatment by police. What followed was an extraordinary year as pro-democracy rebellions erupted across the Middle East. Our interactive timeline traces key events